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A STABLE MASS-FLOW-WEIGHTED TWO-DIMENSIONAL SKEW UPWIND SCHEME

Yassin A. Hassan, J.G. Rice, J. H. Kim

Open publisher page 36 citations

Abstract

A new simple stable approach to the numerical solution of problems in fluid flow and heat transfer has been developed. The new approach avoids the stability problems of the skew upwind difference scheme while reducing the inaccuracies of numerical diffusion associated with upwind differencing. The origin of the instability is examined. Skew upwind differencing is compared with the proposed scheme for some idealized numerical results. The numerical computations presented show the superiority of the new scheme with respect to the shortcoming noted for the skew upwind scheme.

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What this paper is about

A new simple stable approach to the numerical solution of problems in fluid flow and heat transfer has been developed. The new approach avoids the stability problems of the skew upwind difference scheme while reducing the inaccuracies of numerical diffusion associated with upwind differencing. The origin of the instability is examined. Skew upwind differencing is compared with the proposed scheme for some idealized numerical results. The numerical computations presented show the superiority of the new scheme with respect to the shortcoming noted for the skew upwind scheme.

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OpenAlex reports 36 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A new simple stable approach to the numerical solution of problems in fluid flow and heat transfer has been developed. The new approach avoids the stability problems of the skew upwind difference scheme while reducing the inaccuracies of numerical diffusion associated with upwind differencing. The origin of the instability is examined. Skew upwind differencing is compared with the proposed scheme for some idealized numerical results. The numerical computations presented show the superiority of the new scheme with respect to the shortcoming noted for the skew upwind scheme.

Key concepts: Upwind scheme, Skew, Numerical diffusion, Mathematics, Computation, Applied mathematics, Flow (mathematics), Numerical analysis

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